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Is that Ok to exclude fixed components from an objective function?

Suppose we have the following objective function with one decision variable $x_i$ where $p_i$ is a fixed parameter for each $i$ and also, $a$ is a constant for the problem \begin{align} \label{eq} \max \sum^N_{i=1} p_i(a+1-x_i) = \max…
OR Junior
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Model "if and only if" indicator constraints in Linear programming

Apologies if this question has been asked, but I haven't been able to find it. I'm modelling something with Gurobi and want to do the following: \begin{align}\text{cond} < \dfrac{1}{3} &\iff x = 1,\\\dfrac{1}{3} \leq \text{cond} \leq \dfrac{2}{3}…
J. Dionisio
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Concorde with Apple Silicon M1

I am trying to install Concorde linked with QSOPT following these instructions. Regarding QSOPT, I downloaded files from section Intel MacOS 10.6 (64-Bit). But, as I have Apple M1 chip, it does not work. I think that the problem is in the arm64…
Eleonora
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Which software to use for Voronoi diagrams?

I have recently been looking at some facility location problems and how they change in the presence of the motorway (or highway, freeway) etc. Tried to visualize some observations with the Voronoi diagrams. But doing it by hand becomes extremely…
bajun65537
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What are some references for Fluid and Diffusion models in Queuing?

In queuing theory and stochastic process, there are many papers that have applied fluid and diffusion models to approximate the original models. However, the concepts and basics of these models are not comprehensively discussed. I would be thankful…
Amin
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Black-box optimization of a single parameter function with high cost evaluation

I need to solve a series of single parameter black-box minimization problem. The underlying cost functions are quite simple. They always have the same shape: a global minimum inside a fixed interval (-15000; 15000). The constraints are : The…
Kh4zit
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Find Extreme direction of equality constraints

I think this is a very basic question, but I failed to find an algorithm for this... When I have a set of inequality constraints, $Ax \leq b$ as my feasible region, I can set $b = 0$ and find $n-1$ independent rows to solve for an extreme direction,…
PetaGlz
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What is a good way to penalise LP relaxation?

I have a binary integer program. It is of a large size and the solver is taking longer time. I am thinking of relaxing the binary integer variable and making it a continuous variable. How can I penalise the objective function?
KGM
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Quickest shortest path algorithm

I want to do a shortest path algorithm. My direct and not acyclic graph contains only positive numbers. I have to do the scan for all pairs of nodes in complete depth in python. My graph is big (100x100x100 (with time-steps) and I have to do it in a…
maxmitz
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What kind of algorithm is this: water foraging

I am pondering if a machine learning problem might be better formulated as a reinforcement or control problem. I have no experience with the latter, so bear with me. Let's say I am organising a tour and each time the tour has a different number of…
spdrnl
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How to model this multi-commodity flow problem with a twist?

Problem description I am working on a variation of the multicommodity flow problem on a graph $G=(V,E)$. I have requests $r_{uv}$ for pairs of nodes $(u,v), u\in V, v\in V$, which means that $r_{uv}$ units of flow must be shipped from node $u$ to…
Kuifje
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Asymmetric time-constrained capacitated vehicle routing problem

I am trying to add some more constraints to the flow-based ADVRP model in Almoustafa et al. (2013)1 (pp.4). The mentioned model caps the travel distance, while I cap the travel time. Let $U$ represent the maximum travel time each vehicle can make.…
tcokyasar
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Finding the global minimum of $f(\mathbf{x})=\|(1-x_1,x_1-x_2,x_2-x_3,\ldots,x_{n-1}-x_n,x_n-2)\|_2^2$

I am self-learning optimization algorithms. A certain assignment problem is as follows: Show that the $n$-dimensional function $f(\mathbf{x})=\|(1-x_1,x_1-x_2,x_2-x_3,\ldots,x_{n-1}-x_n,x_n-2)\|_2^2$ has exactly one stationary point which is a…
Quasar
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Extreme points of a simple polyhedron

Consider the polyhedron given by the set of inequalities \begin{align} \mathbf{b}^T\mathbf{x} ~&\leq~ c \\ \mathbf{e}^T\mathbf{x} - 1 ~&\leq~0 \\ \mathbf{x}~&\geq~0 \end{align} where $\mathbf{x}\in\mathbb{R}^d$, $\mathbf{b}$ is a given element-wise…
dineshdileep
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How to minimize the number of breaks in sports scheduling?

I have the following sports scheduling problem. For $n$ teams and $m$ rounds, I define the binary decision variable $$ x_{i,j,s} = \text{1 if team $i$ plays at home against team $j$ at round $s$, 0 otherwise}. $$ and the…
Ronaldinho
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